Cut baguette into 1-inch cubes and (if not dry) toast in 200 degree oven for about 10 minutes, until bread is dry, like day-old bread. Turn oven up to 400 degrees. Toss squash with 1 tbsp olive oil on rimmed baking sheet, sprinkle with salt and pepper, and bake until squash is tender, about 20-25 minutes. Turn with spatula occasionally.

Heat about 2 tbsp oil in large pot over medium-high heat. Add shallots and saute until soft, about 5 minutes. Add kale. Cover and cook 2 minutes. Uncover and stir until kale is wilted but still bright green, about 5 minutes. (I cook mine longer, though, because I like the kale less crunchy.)

Reduce oven temperature to 350. Generously butter 13x9x2-inch baking dish. Spread half of bread cubes in the bottom, topped with half of kale mixture, then half of squash, and sprinkled with half of cheese. Repeat with remaining bread, kale, squash, and cheese. Pour egg mixture over the bread pudding. Cover with foil and bake for 20 minutes. Remove foil and bake uncovered until custard is set and bread feels springy to the touch, about 20 minutes longer. Broil 2 minutes right before serving until cheese browns slightly.

Notes:
*I don't like soggy bread pudding, so I altered the original recipe a little. Here are the things I did, so you can decide how you like it best.
* The recipe didn't call to toast the bread, just to cut it up, but I like it more stale.
*The recipe said to soak the bread in the egg mixture for 30 minutes before baking, but I completely skipped this step because I didn't want all soggy bread.
* When I did finally pour the egg mixture in the pan right before baking, I made sure not to completely cover the top pieces of bread, making sure they were still dry on top.
* I used more cheese